
Contrary to existing works such as [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, which relied on time division duplexing (TDD) transmission for IRS-assisted systems, we consider FDD. To the best of our knowledge, there are no prior works accounting for FDD in IRS and studying its performance except of [10]}, [11]}, [12]}. Especially, [10]} proposed a cascaded codebook and an adaptive bit partitioning strategy, [11]} considered a two-way passive beamforming design, and [12]} proposed a dimension reduced channel feedback scheme to reduce the channel feedback overhead in RIS assisted systems.

This is the first work applying the concept of JSDM [16]} on IRS-assisted systems to reduce the feedback overhead being increasingly significant with the numbers of antennas and IRS elements. In particular, not only do we study the performance but we also provide system guidelines concerning the choice of JSDM parameters. Moreover, we have generalized [16]} since we do not assume equal power among the UEs but perform power optimization.

Although many previous works were based on I-CSI knowledge and independent Rayleigh fading such as [18]}, [19]}, [20]}, we move towards consideration of realistic conditions and we hinge on S-CSI (more advantageous) and correlated Rayleigh fading, which is unavoidable as shown in [21]}. Remarkably, based on the use of S-CSI and the effective channel, consisting of the cascaded and direct channels, we achieve to obtain the achievable SE of IRS-assisted systems similar to conventional systems. Notably, works considering S-CSI and correlated Rayleigh fading exist (e.g., [5]}, [6]}, [7]}, [9]}) but none of them has accounted for the JSDM approach.

By employing the per-group processing (PGP) method of the JSDM approach to reduce the feedback overhead [16]}, we derive the sum SE of the IRS-assisted mMIMO systems based on FDD in closed-form by leveraging results from the deterministic equivalent (DE) analysis [27]}, [28]}, [29]}. The importance of the results in terms of DEs is noteworthy since DEs provide an analytical tool resulting in a deterministic expression of the SE based on a convergent system of fixed-point equations while avoiding lengthy Monte Carlo simulations.

We formulate the optimization problem concerning the sum SE subject to reflecting beamforming matrix (RBM) and total transmit power constraints. Note that the PGP method includes the regularized zero-forcing (RZF) precoding and this is the unique work providing RBM optimization based on S-CSI with such a complex precoder. Other works such as [5]} considered a simple linear precoding, e.g., maximum ratio transmission (MRT) precoding. Furthermore, the proposed optimization is based on deterministic expressions dependent only on large-scale statistics, and thus, can be performed at every several coherence intervals and reduce considerably the signal overhead as required especially in FDD systems.

We verify the results by Monte-Carlo (MC) simulations and we shed light on the impact of the system parameters on the sum SE such as the signal-to-noise ratio (SNR), the effective covariance rank, the effective channel dimension, and the number of IRS elements. Especially, the effective covariance rank and effective channel dimension play a prominent role by presenting a trade-off between the feedback reduction and the performance.

